Phonons and Crystal Field Levels in Dysprosium Garnets by Raman Scattering

Raman scattering from DyA1 and DyGa garnets at 80 K was investigated to determine the Raman-active phonons ($3A_{1g}+8\mathrm{}{E}_g+14\mathrm{}{T}_{2g}$) and the ${}_{}{}^6{}_{}{}^{}H_{\frac{15}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$ crystal field levels. The frequencies and the symmetries of all the Raman-active phonons in DyGa garnets and all except one phonon in DyAl garnets were determined. The positions of the lowest four levels in the ${}_{}{}^6{}_{}{}^{}H_{\frac{15}{2}}^{}{}_{}{}^{}$ manifold and all seven levels in the ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$ manifold were measured in DyAl and DyGa garnets. For DyAl garnets, the ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$ manifold has hitherto not been observed. A full crystal field calculation was carried out using our Raman data on the ${}_{}{}^6{}_{}{}^{}H_{\frac{15}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$ manifolds along with the absorption data of Grünberg et al. and of Aoyagi et al. on the other higher-energy crystal field levels. The crystal field Hamiltonian appropriate for the $D_2$ symmetry of the rare-earth sites was used, and the mixing of the different $J$ states by the crystal field was included. The best-fit values for the nine crystal field parameters plus the free-ion energies were found. These values were similar to those obtained by Grünberg et al. for the dilute garnets YAlG(Dy) YGaG(Dy). The relative electronic Raman intensities, measured for our selected combinations of incident and scattered polarizations, are listed. It is shown how these intensities are related to the Raman-scattering tensors, which in turn depend on the crystal field eigen-functions. In principle, the Raman intensity ratios can provide a good test of the crystal field analysis, analogous to the role of the $g$ tensor.